Question

An object moves at a constant speed along a circular path in a horizontal $XY$ plane. With the center at the origin. When the object is at $x=-2m$, its velocity is $-\left(4m/s\right)\hat{j}$. What is the object's acceleration when it is $y=2m$:

• A. $-\left(8m/s^2\right)\hat{j}$
• B. $\left(8m/s^2\right)\hat{i}$
• C. $-\left(4m/s^2\right)\hat{j}$
• D. $\left(4m/s^2\right)\hat{i}$

Answer 1

The correct option is A $-\left(8m/s^2\right)\hat{j}$

Velocity , v=$-\left(4m/s\right)\hat{j}$

at $y=2$ , centripetal acceleration magnitude,

$\begin{array}{c}a=\frac{v^2}{r}\\ =\frac{{\left(4\right)}^2}{2}\\ =\frac{16}{2}=8m/s^2\end{array}$

So $a_r=-\left(8m/s^2\right)\hat{j}$